Related papers: A Guide to the Bott Index and Localizer Index
Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific…
Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a…
We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie…
In this note, we study the local properties of the Chern-scalar curvature function by looking at its linearization. In particular, we study its linearization stability and the structure of the space of Hermitian metrics with prescribed…
The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications…
Parameterized stable homotopy theory organizes local systems of spectra over homotopy types, governed by a "yoga" of six functors. To provide semantics for the recently developed Linear Homotopy Type Theory (LHoTT), good model categories of…
In this note, we investigate the structural controllability and observability indices of structured systems. We provide counter-examples showing that an existing graph-theoretic characterization for the structural controllability index…
Driven optical lattices permit the engineering of effective dynamics with well-controllable tunneling properties. We describe the realization of a tunable a Chern insulator by driving particles on a shaken hexagonal lattice with optimally…
The spectral localizer, introduced by Loring in 2015 and Loring and Schulz-Baldes in 2017, is a method to compute the (infinite volume) topological invariant of a quantum Hamiltonian on $\ZZ^d$, as the signature of the (finite) localizer…
We propose an alternative formulation of the $Z_2$ topological index for quantum spin Hall systems and band insulators when time reversal invariance is not broken. The index is expressed in terms of the Chern numbers of the bands of the…
It is argued that Bell's nonlocality is a particular case of nonlocality at detection, which appears already in single-particle interference experiments. The unity of nonlocality and local causality is crucial to provide a consistent…
The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is…
Recent work on Vision Transformers (VTs) showed that introducing a local inductive bias in the VT architecture helps reducing the number of samples necessary for training. However, the architecture modifications lead to a loss of generality…
We study topological properties of the Bose-Hubbard model with repulsive interactions in a one-dimensional optical superlattice. We find that the Mott insulator states of the single-component (two-component) Bose-Hubbard model under…
We introduce the electronic polarization originally defined in one-dimensional lattice systems to characterize two-dimensional topological insulators. The main idea is to use spiral boundary conditions which sweep all lattice sites in…
We prove a local-global principle for $\infty$-categories over any base $\infty$-category $\mathcal{C}$: we show that any $\infty$-category $\mathcal{B} \to \mathcal{C}$ over $\mathcal{C}$ is determined by the following data: the collection…
Recommending points of interest (POIs) is a challenging task that requires extracting comprehensive location data from location-based social media platforms. To provide effective location-based recommendations, it's important to analyze…
This paper studies the average gradient over the local region of a function and constructs the homogenization function of a function. It is found that there are some good properties about the local extreme points and the global extreme…
Chern insulators are states of matter characterized by a quantized Hall conductance, gapless edge modes but also a singular response to monopole configurations of an external electromagnetic field. In this paper, we describe the nature of…
Localization in the environment is an essential navigational capability for animals and mobile robots. In the indoor environment, the global localization problem remains challenging to be perfectly solved with probabilistic methods.…